Subgroups — D₁₆×D₁₂₇ #22550295

Order 8128.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₁₂₇	C₂	1	2	yes	maximal, complemented
2	D₂₀₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#16861150	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₁₂₇	—	2	2	no	—
7	D₁₀₁₆	C₂²	1	2	yes	complemented
8	#14523233	—	2	2	no	—
9	C₈×D₁₂₇	C₂²	1	1	yes	characteristic
10	C₁₂₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₁₂₇	C₂²	1	2	yes	complemented
12	C₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₁₂₇	—	4	2	no	—
14	D₅₀₈	—	2	2	no	—
15	C₂²⋊D₁₂₇	—	4	2	no	—
16	C₄×D₁₂₇	D₄	1	1	yes	characteristic
17	C₁₂₇⋊C₈	D₄	1	1	yes	characteristic
18	D₄×C₁₂₇	—	2	2	no	—
19	C₈×C₁₂₇	C₂³	1	1	yes	characteristic
20	C₂²×C₁₂₇	—	4	2	no	—
21	C₂×D₁₂₇	—	4	2	no	—
22	C₂×D₁₂₇	—	8	4	no	—
23	C₂×D₁₂₇	D₈	1	1	yes	characteristic
24	C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
25	Dic₁₂₇	D₈	1	1	yes	characteristic
26	C₂×C₁₂₇	—	8	2	no	—
27	C₂×C₁₂₇	C₂×D₈	1	1	yes	characteristic
28	D₁₂₇	—	8	2	no	—
29	D₁₂₇	D₁₆	1	2	yes	direct product factor
30	C₁₂₇	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	127	1	no	maximal, Sylow
32	C₂×D₈	—	127	2	no	—
33	D₁₆	—	127	2	no	—
34	D₁₆	—	127	1	no	—
35	D₁₆	D₁₂₇	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	127	1	no	—
37	C₂×D₄	—	254	2	no	—
38	D₈	—	127	2	no	—
39	D₈	—	254	2	no	—
40	D₈	C₂×D₁₂₇	1	2	yes	complemented
41	C₂×C₈	—	127	1	no	—
42	C₁₆	—	127	1	no	—
43	C₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
44	C₂³	—	508	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	508	2	no	—
47	D₄	—	254	2	no	—
48	C₂×C₄	—	127	1	no	—
49	C₈	—	127	1	no	—
50	C₈	C₂²×D₁₂₇	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	127	1	no	—
53	C₂²	—	1016	4	no	—
54	C₂²	—	508	2	no	—
55	C₄	—	127	1	no	—
56	C₄	D₄×D₁₂₇	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	127	2	no	—
59	C₂	—	1016	2	no	—
60	C₂	D₈×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₂₇
commutator	C₈×C₁₂₇	C₂³
Frattini	C₈	C₂²×D₁₂₇
Fitting	D₁₆×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂×D₈
hypercenter	D₁₆	D₁₂₇
hypocenter	C₁₂₇	C₂×D₁₆
LCS	G ▷ C₈×C₁₂₇ ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₈×D₁₂₇	C₂	semidirect
2. D₂₀₃₂	C₂	semidirect
3. #16861150	C₂	semidirect
4. C₁₆×D₁₂₇	C₂	semidirect
5. D₁₆×C₁₂₇	C₂	semidirect
7. D₁₀₁₆	C₂²	semidirect
10. C₁₂₇⋊C₁₆	C₂²	semidirect
11. D₈×C₁₂₇	C₂²	semidirect
12. C₁₆×C₁₂₇	C₂²	semidirect
29. D₁₂₇	D₁₆	direct (N × H)
30. C₁₂₇	C₂×D₁₆	semidirect
35. D₁₆	D₁₂₇	direct (N × H)
40. D₈	C₂×D₁₂₇	semidirect
43. C₁₆	C₂×D₁₂₇	semidirect

Subgroups — D16×D127 #22550295

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×D₁₂₇ #22550295